Question

Suppose Musashi and Rina are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Musashi chooses Right and Rina chooses Right, Musashi will receive a payoff of 3, and Rina will receive a payoff of 7.

Rina Rina
Left Right
Musashi Left 4, 3 6,1
Musashi Right 7,6 4,4
The only dominant strategy in this game is for _____ to choose _____.
The outcome reflecting the unique Nash equilibrium in this game is as follows: Musashi chooses _____and Rina chooses _____.

Answer 1

See explaination

Step-by-step explanation:

a) A dominant strategy is the strategy a player chooses irrespective of the strategy chosen by the other player.

When Rina chooses Left, Musahi chooses Right as this gives higher payoff (7 > 4).

When Rina chooses Right, Musahi chooses Left as this gives higher payoff (6 > 3).

When Musahi chooses Left, Rina chooses Right as this gives higher payoff (8 > 6).

When Musahi chooses Right, Rina chooses Right as this gives higher payoff (7 > 5).

So, the only dominant strategy is for Rina to choose Right.

(b) In a Nash equilibrium, the players decide their strategies keeping in mind the reaction of the other strategy.

Here, this is: Musahi chooses Left & Rina chooses Right (payoff: 6, 8).